We have developed a powerful 3D Monte Carlo code, as part of the Radiance in a Dynamic Ocean (RaDyO) project, which can compute the complete effective Mueller matrix at any detector position in a completely inhomogeneous turbid medium, in particular, a coupled atmosphere-ocean system. The light source can be either passive or active. If the light source is a beam of light, the effective Mueller matrix can be viewed as the complete impulse response Green matrix for the turbid medium. The impulse response Green matrix gives us an insightful way to see how each region of a turbid medium affects every other region. The present code is validated with the multicomponent approach for a plane-parallel system and the spherical harmonic discrete ordinate method for the 3D scalar radiative transfer system. Furthermore, the impulse response relation for a box-type cloud model is studied. This 3D Monte Carlo code will be used to generate impulse response Green matrices for the atmosphere and ocean, which act as inputs to a hybrid matrix operator–Monte Carlo method. The hybrid matrix operator–Monte Carlo method will be presented in part II of this paper.
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